Calculator
Add solid parts. Subtract holes, notches, and empty regions. Use one measurement unit for all dimensions.
Dimension Guide
| Shape | Value A | Value B | Value C |
|---|---|---|---|
| Rectangle | Length | Width | Not used |
| Triangle | Base | Height | Not used |
| Circle | Radius | Not used | Not used |
| Semicircle | Radius | Not used | Not used |
| Trapezoid | Base one | Base two | Height |
| Parallelogram | Base | Height | Not used |
| Ellipse | Semi-major axis | Semi-minor axis | Not used |
| Circle Sector | Radius | Not used | Angle in degrees |
| Annulus | Outer radius | Inner radius | Not used |
| Regular Polygon | Side length | Not used | Number of sides |
| Custom Area | Known area | Not used | Not used |
Example Data Table
| Component | Shape | Operation | Values | Area |
|---|---|---|---|---|
| Main figure | Rectangle | Add | A = 10, B = 8 | 80.000 square units |
| Corner cutout | Rectangle | Subtract | A = 4, B = 3 | -12.000 square units |
| Rounded end | Semicircle | Add | A = 2 | 6.283 square units |
| Total | 80 - 12 + 6.283 | 74.283 square units | ||
Formula Used
The calculator finds each component area first. It then applies the selected operation.
Total composite area = sum of added areas − sum of subtracted areas
- Rectangle: A = length × width
- Triangle: A = 1/2 × base × height
- Circle: A = πr²
- Semicircle: A = 1/2 × πr²
- Trapezoid: A = 1/2 × (base one + base two) × height
- Ellipse: A = πab
- Sector: A = (angle ÷ 360) × πr²
- Annulus: A = π × (outer radius² − inner radius²)
How to Use This Calculator
- Sketch the composite figure.
- Split it into simple shapes.
- Select Add for solid parts.
- Select Subtract for holes and missing parts.
- Enter values using the dimension guide.
- Choose unit and decimal places.
- Press Calculate area.
- Use CSV or PDF buttons to save the result.
Composite Figure Area Guide
What This Calculator Does
Composite figures are built from two or more simple shapes. A patio plan may combine rectangles, triangles, circles, and cutouts. A floor plan may subtract stair wells, columns, or curved openings. This calculator helps you break that figure into clear pieces. It adds solid parts. It subtracts holes. It then shows every line of the area work.
Why It Helps
The tool is useful for class work and practical design. You can model rectangles, triangles, trapezoids, circles, sectors, ellipses, annuli, regular polygons, and custom areas. Each row acts like one part of the drawing. Choose Add for visible material. Choose Subtract for empty space or removed material. The signed area column explains how the total was formed.
Plan Before Entry
A composite area problem becomes simple when you sketch first. Draw boundary lines that split the figure into known shapes. Label each needed dimension. Use the same unit for every measurement. If a dimension is missing, find it from the drawing before calculating. This avoids mixed values and double counting.
Export and Review
This page also supports records. The CSV option creates spreadsheet friendly data. The PDF option creates a simple report. These exports help teachers, students, estimators, and designers keep a clean audit trail. You can compare several layouts by changing rows and saving each result.
Accuracy Tips
Composite area answers are only as accurate as the entered dimensions. Use measured values when possible. Use consistent rounding. Keep enough decimal places for curved shapes because pi based formulas can change the final area. For construction or costing, add waste or safety factors outside the pure geometry result.
Best Practice
The best method is to start with the largest shapes. Add them first. Then subtract holes, notches, and internal openings. Review the component table after calculation. If the signed area looks wrong, check the operation and dimensions. A subtraction row should usually represent a smaller area than the main figure.
Flexible Uses
By using rows instead of a single rigid diagram, this calculator covers many composite figures. It works for worksheets, gardens, tiles, plates, signs, rooms, machine parts, and mixed geometry practice. It also supports quick peer review. Another person can read the entries, formulas, and totals without seeing your original sketch. That makes mistakes easier to spot before submitting, ordering, cutting, or budgeting materials.
FAQs
What is a composite figure?
A composite figure is a shape made from two or more simple shapes. Common parts include rectangles, triangles, circles, and trapezoids.
When should I subtract an area?
Subtract an area when the part is empty, removed, cut out, or not included in the final region.
Can I use different units in one calculation?
No. Convert all dimensions to the same unit before entry. Mixed units will give a wrong total.
How do I calculate an L-shaped area?
Use a large rectangle, then subtract the missing rectangle. You can also split the L shape into two rectangles and add them.
What does signed area mean?
Signed area shows whether a component increased or decreased the total. Added parts are positive. Subtracted cutouts are negative.
Can I enter a known area directly?
Yes. Choose Custom Area. Enter the known area in Value A. Then choose Add or Subtract.
Why is my sector result wrong?
Check that Value C is the angle in degrees. The calculator accepts sector angles from greater than zero up to 360 degrees.
Does the PDF include all component rows?
Yes. The PDF report includes the total, shape names, operations, formulas, dimensions, and signed areas for entered rows.